Ordinal-ResLogit: Interpretable Deep Residual Neural Networks for Ordered Choices

Abstract

This study presents an Ordinal version of Residual Logit (Ordinal-ResLogit) model to investigate the ordinal responses. We integrate the standard ResLogit model into COnsistent RAnk Logits (CORAL) framework, classified as a binary classification algorithm, to develop a fully interpretable deep learning-based ordinal regression model. As the formulation of the Ordinal-ResLogit model enjoys the Residual Neural Networks concept, our proposed model addresses the main constraint of machine learning algorithms, known as black-box. Moreover, the Ordinal-ResLogit model, as a binary classification framework for ordinal data, guarantees consistency among binary classifiers. We showed that the resulting formulation is able to capture underlying unobserved heterogeneity from the data as well as being an interpretable deep learning-based model. Formulations for market share, substitution patterns, and elasticities are derived. We compare the performance of the Ordinal-ResLogit model with an Ordered Logit Model using a stated preference (SP) dataset on pedestrian wait time and a revealed preference (RP) dataset on travel distance. Our results show that Ordinal-ResLogit outperforms the traditional ordinal regression model for both datasets. Furthermore, the results obtained from the Ordinal-ResLogit RP model show that travel attributes such as driving and transit cost have significant effects on choosing the location of non-mandatory trips. In terms of the Ordinal-ResLogit SP model, our results highlight that the road-related variables and traffic condition are contributing factors in the prediction of pedestrian waiting time such that the mixed traffic condition significantly increases the probability of choosing longer waiting times.